The good news is the answer is yes as Legendary CEO Thomas Tull confirms that Gareth Edwards will be back for more Godzilla sequels with a report at THR stating Edwards is actually attached to twomore Godzilla movies.

Tull released the following in response to the Star Wars news:

"Gareth's filmmaking talent makes him one of his generation's most creative and visionary directors. The plan has always been for Gareth to direct a different film before we started on another Godzilla, but who knew it would a Star Wars installment? We have a great plan in store for Godzilla fans and I am looking forward to seeing Gareth’s imprint on the Star Wars universe."

It's reported Gareth Edwards is attached to Godzilla 2 and 3, but regarding the sequel a script isn't even ready as of yet.